Answer
$\dfrac{117 \pi}{5}$
Work Step by Step
Area $=R^2\pi- r^2 \pi=\pi (8+6x-x62-x^4)$
We integrate the integral to calculate the volume as follows:
$V= \pi \times \int_{-1}^{2} (8+6x-x62-x^4) dx$
Now, $V= \pi [8+3x^2-\dfrac{x^3}{3}-\dfrac{x^5}{5}]_{-1}^{2}$
or, $= \pi (30-\dfrac{33}{5})$
or, $=\dfrac{117 \pi}{5}$
